Probe for surface measurement

ABSTRACT

A surface-measuring apparatus comprising a probe and means for moving the probe towards and away from a surface under examination and for monitoring such movement, the probe comprising a plurality of closely spaced light-collecting elements arranged in a light-collecting plane, lens means positioned to produce a sharply focussed image of said light collecting elements at an image plane movable relative to said surface by movement of the probe, illuminating means so arranged that the lens unit forms an illuminated spot image of it in the image plane in co-incidence with the image In the image plane of one of the light-collecting elements, and means for measuring the incidence of light on the said one of the light-collecting elements and on surrounding ones of those elements. In one embodiment (FIG. 1) the probe incorporates a bundle of, say, seven optical fibers which each have one end exposed at an end plane of the bundle and constituting a respective one the light-collecting elements, the fibers being connected at their other ends to photodiodes or other photodetector means for measuring the Incidence of light on the exposed ends of the fibers. In another embodiment, the light-collecting elements are the individual detector cells comprised in the detector array of a solid state camera, the cells being organized in groups each having a central cell and a plurality of surrounding cells, and the illuminating means may be a screen with appropriately located apertures illuminated from behind.

This invention relates to apparatus for carrying out measurements toestablish the form or profile, or the texture, of a surface.

Traditionally, the measurement of surface form has been effected bymeans of mechanical sensors or probes which make contact with thesurface being investigated and which, though yielding accurate results,are inherently slow in operation and limited in spatial resolution.There have therefore been various proposals and attempts to make use ofoptical sensors in the measurement of surface form, since these ingeneral can have higher speeds of operation than mechanical probes and,moreover, they do not make mechanical contact with the surface and boththe probe and the surface are thereby protected from possible damage ordeformation. However, optical probes (including fiber-optic probes) arenot widely used, principally because the performance of such probes ofknown kinds is strongly affected by variations in the reflectivity,scattering properties and surface texture characteristics of the surfaceunder investigation. This severely limits the range of applicability ofsuch probes: typically, problems are encountered in attempting to employoptical probes in the measurement of surfaces which are matt black orhighly polished or are of such materials as perspex or nylon.

It is an object of the present invention to provide apparatus, whichincludes a fiber-optic or comparable optical probe, for carrying outmeasurements to establish the form, profile or texture of a surface andof which the performance is in large measure independent of thereflectivity of such surface.

According to the invention there is provided surface-measuring apparatuscomprising a probe and means for moving the probe towards and away froma surface under examination and for monitoring such movement, the probecomprising a plurality of closely spaced light-collecting elementsarranged In a light-collecting plane, lens means positioned to produce asharply focussed image of said light collecting elements at an imageplane movable relative to said surface by movement of the probe,illuminating means so arranged that the lens unit forms an illuminatedspot image of it in the image plane in co-incidence with the image inthe image plane of one of the light-collecting elements, and means formeasuring the incidence of light on the said one of the light-collectingelements and on surrounding ones of those elements.

In one embodiment of such apparatus, the probe incorporates a bundle of,say, seven optical fibers which each have one end exposed at an endplane of the bundle and constituting a respective one of thelight-collecting elements, the fibers being connected at their otherends to photodiodes or other photodetector means for measuring theincidence of light on the exposed ends of the fibers. The fiber whoseone end constitutes the said one of the light-collecting elements may becoupled both to the respective photodetector means and to a source ofillumination, which may be a laser diode, whereby the one end of thefiber also constitutes the illuminating means. Alternatively, betweenthe lens means and the light-collecting plane in which thelight-collecting elements are disposed there may be interposed a beamsplitter which enables the illuminating means to be physically separate,constituted for example by an optical fiber having one of its endscoupled to the laser diode and its other end positioned so that itsImage in the beam splitter is superposed on the said one of thelight-collecting elements.

In another embodiment of apparatus according to the invention, thelight-collecting elements are the individual detector cells comprised inthe detector array of a solid state camera. The detector cells of suchan array may be organized in groups each having a central cell and aplurality of surrounding cells, and the illuminating means may be ascreen with appropriately located apertures illuminated from behind, soplaced relative to a beam-splitter arranged between the detector arrayand the lens means that the images of the illuminted apertures in thebeam splitter coincide with the central cells of the respective groups.

The invention will be more fully understood from the followingdescription of preferred embodiments thereof with reference to theaccompanying drawings, in which:

FIG. 1 is a schematic representation of a probe of apparatus accordingto the invention, positioned over a surface of which the form or profileis to be measured by means of the apparatus;

FIG. 2 is an end view, on a larger scale, of a bundle of optical fiberscomprised by the probe shown in FIG. 1;

FIG. 3 is a ray diagram relating to the formation of optical images bythe probe shown in FIG. 1;

FIG. 4 shows curves relating to the distribution of light on the end ofa bundle of optical fibers comprised by the probe shown in FIG. 1;

FIG. 5 is a schematic representation of apparatus which incorporates aprobe similar to that shown in FIG. 1 but including modifications; and

FIG. 6 is a schematic representation of an embodiment of apparatusaccording to the invention, having a probe which incorporates, insteadof optical fibers with associated detector cells, a solid-state cameradetector array having a large number of individual detector cells.

The optical probe shown schematically in FIG. 1 and indicated generallyby reference numeral 10 comprises a mechanical housing 11 having a frontwall in which is mounted a lens unit 12, which is shown as consisting ofa pair of lenses 12a and 12b though these can be regarded as effectivelyconstituting a single lens. Also mounted in the housing 11, coaxial withthe lens unit 12, is one end of an optical fiber bundle 13 composed, asshown in FIG. 2, of a central circular-section fiber 14 and six outercircular-section fibers 15 secured in a uniform hexagonal array aboutthe fiber 14, all the fibers being of equal diameters of, say, 0.5 mm.The fibers, exposed at an end face 13' of the bundle 13, as shown inFIG. 2, may be polymer Eska fibers and may be embedded In a matrix 16 ofglue or cement, within a surrounding ferrule 17 by means of which theend face 13' may be positively located relative to the lens unit 12.

Mounted In the housing 11 between the lens unit 12 and the end face 13'of the fiber bundle is a beam splitter 18, and a further optical fiber19 is so mounted in the housing that an image of its end face 19' in thebeam splitting surface 18' of the beam splitter 18 coincides with theend face of the fiber 14 in the end face 13' of the fiber bundle 13.

At its end remote from its end face 19', the fiber 19 is coupled to asource of illumination, which may be a laser diode 20, and light fromthis source emerging from the fiber end face 19' is reflected in thebeam splitter 18 and passes through the lens unit 12, as if It hademanated from the fiber 14, to provide a spot of illumination on asurface 21 which Is to be investigated. Light from the illuminated spot,passing again through the lens unit 12 and through the beam splitter 18,is incident on the end face 13' of the bundle 13, and in general (aswill be explained below) enters both the central fiber 14 of the bundleand the outer fibers 15. For sensing this light, the fiber 14 at its endremote from the end face 13' is coupled to a photo-detector 22, and thefibers 15 are similarly coupled to a photo-detector 23.

The fiber 19 and beam splitter 18 enable light to be launched into thesystem as though from the fiber 14, and in an alternative but equivalentarrangement the laser diode 20 may in fact be coupled to the fiber 14which then serves both to launch light into the system and to receivelight back. In that alternative, the beam splitter 18 and the fiber 19are omitted. It is then necessary to provide, in known manner, a couplerby means of which the fiber 14 is coupled both to the laser diode 20 andto the photo-detector 22; but the omission of the beam splitter meansthat this modification has considerable advantage in practice since theprobe can be made much smaller, and cheaper.

The optical behaviour of the probe shown in FIG. 1 may be explained byreference, first, to FIG. 3, in which the lens unit 12 is represented bya thin lens of focal length f, in the plane LL and with focal points Fand F', and O is an object in the end plane 13' of the fiber bundle 13.If the object distance of the object O is S_(o), the lens forms an imageI₁ at an image distance S₁, where

    1/S.sub.1 =1/S.sub.o +1/f.                                 (1)

Supposing the surface 21 is more distant, by a distance x, from the lensplane LL than is the image I₁, and that the surface 21 ismirror-reflective, then the light focussed by the lens to form the imageI₁ is reflected by the surface 21 and re-enters the lens as though ithad emanated from a virtual image I' of the image I₁, the image I' beingat a distance S₁ +2x from the lens. The lens forms a further image I₂ ofthe image I', the image I₂ being at a distance S₂ from the lens, where

    1/S.sub.2 =1/(S.sub.1 +2x)-1/f                             (2)

and thus at a distance x_(o) from the end plane 13' of the fiber bundle13, where

    x.sub.o =S.sub.o -S.sub.2.                                 (3)

Substitution In equation (3) of expressions for S_(o) and S₂ derivedfrom equations (1) and (2) give:

    x.sub.o =2xf.sup.2 /(S.sub.1 -f).(S.sub.1 +2x-f).          (4)

If h_(o), h₁ and h₂ are the heights of the object O and of the image I₁(and I') and I₂ respectively, then:

    h.sub.1 /(S.sub.1 -f)=h.sub.o /f

and

    h.sub.2 /(S.sub.2 =h.sub.1 /(S.sub.1 +2x)

from which:

    h.sub.2 =h.sub.o (S.sub.1 -f)S.sub.2 /f(S.sub.1 +2x)

or, substituting for S₂ the expression which may be derived fromequation (2) above,

    h.sub.2 =h.sub.o (S.sub.1 -f)/(S.sub.1 +2-f).              (5)

It will be seen that equations (4) and (5) define both the position andthe size of the image I₂ in terms of x, and thus of the position of thesurface 21 relative to the probe 10, since f and S_(o) (and thereforealso S₁) are fixed values. It will be seen also that if the probe 10 ispositioned such that the image I₁ Is actually focussed on the surface21, so that x=0, the result is that x_(o) =0 and h₂ =h_(o), which meansthat the image I₂ is formed in the end plane 13' of the fiber bundle 13and coincides with the object of which it is an image. Thus, if theprobe is positioned so that light launched from the central fiber 14(or, equivalently, from the fiber 19 as shown In FIG. 1) is focussedinto an image I₁ on the surface 21 (i.e. x=0), the light reflected backthough the lens to form the image I₂ is focussed in the end plane 13' ofthe fiber bundle 13 entirely on the end of the fiber 14 and none of thereflected light falls on the ends of the outer fibers 15.

If the probe is moved, relative to the surface 21, so that it is nolonger the case that x=0, the image 12 is no longer focussed in theplane 13' and some of the light forming this image will now be incidenton that plane outside the region of the original object O. Thus, asshown in FIG. 3, light focussed at the arrow point of the image I₂ isincident on the plane 13' at a region 24 where it forms a blurred Imageof the arrow point at a greater off-axis distance than the correspondingarrow point of the original object O. Thus some of the light from thefiber 14 (or 19) Is returned, if the surface 21 is not at the positionat which the image I₁ is formed, not to the central fiber 14 but to theouter fibers 15. This effect is shown in FIG. 4, In which the curve 25shows how the intensity of light received by the fiber 14 and sensed bythe sensor 22 is greatest when x=0 and falls off as the probe 10 ismoved from that position towards or away from the surface 21, whereas,as shown by the curve 26, the light incident on the outer fibers 15 andsensed by the sensor 23 is a minimum (zero, in the absence of diffusescattering) for x=0 and rises to maxima on either side of the x=0position before falling off again at greater positive and negativevalues of x.

The equations (4) and (5) above were derived on the assumption that thesurface 21 is a specularly reflective surface. If the surface 21reflects only diffusely, the image I₂ is the image formed by the lensunit 12 not of the virtual image I' but of a blurred-image patch ofillumination of the surface 21 itself (at an object distance of (S₁ +x)instead of (S₁ +2x)) for the image I'. In that case, the equations (4)and (5) no longer apply but corresponding expressions for x_(o) and h₂,the position and height of the image I₂, in terms of x, which definesthe position of the surface 21, are obtainable, thus:

    x.sub.o =xf.sup.2 /(S.sub.1 -f)·(S.sub.1 +x-f)    (6)

and

    h.sub.2 ={A.F.x+h.sub.o S.sub.1 (S.sub.1 -f)}/S.sub.1 (S.sub.1 +x-f)(7)

where A is the aperture of the lens unit 12. It will be seen that inthis case, also, x_(o) =0 and h₂ =h_(o) when x=0, so that light emittedfrom the central fiber 14 will be imaged again only on that fiber andnot on the fibers 15 when the surface 21 is posltioned to have the imageI₁ focussed sharply upon it. For non-zero values of x, the situation Isagain as represented by the curves 25 and 26 of FIG. 4; and the same istrue for surfaces 21 intermediate between the specularly and diffusivelyreflective cases considered.

As shown in FIG. 4, the curves 25 and 26 intersect in two points P₁ andP₂, corresponding with two positions of the probe 10, at differentdistances from the surface 21, at which the light entering the fiber 14and detected by the photo-detector 22 is equal to that entering thefibers 15 and detected by the photo-detector 23. Comparison of theoutput signals of the photo-detectors 22 and 23 enables a difference orerror signal to be derived, which may then be used to control a motorarranged to move the probe towards or away from the surface 21 andmaintain it at a constant distance corresponding to a particular valueof x. If, then, a further drive means is provided for moving the probealong the surface 21, the surface profile along a line on the surfacemay be scanned automatically by measuring the movements of the probe inthe direction towards and away from the surface while the probe isdriven in the direction across the surface.

In another mode of operation, the probe may be driven towards and awayfrom the surface repeatedly, at spaced points thereof. In this mode, ateach approach of the probe to the surface, the two output signals fromthe detectors 22 and 23 first become equal as the point P₂ is reached,and this event may be used either as a measure of the position of thesurface or to trigger the onset of a reduced speed of approach, so thatthe point P₁, at which the detector outputs are again equal, is reachedat low speed and can thus be detected with Increased accuracy, as themeasure of the surface position.

The use of the probe according to the invention in either of these ways,or in other ways which are also possible, is relatively unaffected bythe degrees of reflectivity and absorptivity of the surface to bemeasured, because these qualities affect almost equally the amounts oflight reflected into the central and outer fibers 14 and 15respectively, and it is only the ratio between these amounts which issignificant. Although P₁ and P₂ have been referred to as the points atwhich the photo-detectors 22 and 23 have equal outputs, these outputswill usually be compared after amplification; and they may If desired beamplified with differently chosen amplification factors so as,effectively, to choose the parts of the two curves 25 and 26 at whichthey intersect one another. By this means it is possible to select thoseparts of the curve with the greatest rate of change, thereby achievinghigh sensitivtty.

The relative shapes of the curves 25 and 26 and, in particular, thedistance apart, in the x-direction, of the two maxima of the curve 26,are to some extent dependent on the degree of diffuseness of thereflectivity of the surface 21, and immunity of the results obtained toerror from this cause can be minimised, if desired, by measuring boththe P₁ and the P₂ positions and calculating and using the mean or, moreaccurately, the weighted mean of the two values rather than the actualmeasured value of either one of them.

It will be understood that the resolution of the system depends both onthe magnification produced by the lens unit and on the cross-sectionalarea of the optical fibers, and that apparatus according to theInvention which may be employed, for example, to measure both surfaceform or profile and surface texture may be provided with interchangeablelens units and/or fiber bundles to vary the system resolution asappropriate.

In the probe shown in FIG. 1, the light captured by all the outer fibers15 is summed by a single photo-detector 23, but in a more sophisticatedarrangement the outputs from the fibers 15 may be measured individually.Such an arrangement is shown in FIG. 5, in which similar parts areindicated by the same reference numerals as In FIG. 1. The central fiber14 is coupled to a photo-detector 22, as before, but each of the outerfibers 15 is coupled to a separate respective photo-detector 23a, andthe outputs of the detector 22 and all the detectors 23a are fed toamplifying and processing circuitry 27. In addition, a fiber 28 havingan end mounted in the side of the probe housing 11 picks up light fromthe fiber 19 which is not deflected by the beam splitter 18 and this,detected by a photo-detector 29, provides a reference signal which isalso fed to the circuitry 27. The data provided by the circuitry 27 aretransferred via a data acquisition card 30 to a computer 31, which maysuitably be a personal computer, and there stored and processed,together with data relating to the position of the probe 10 which issupplied to the card 30 by means (not shown) for moving the probe in xand y directions over the surface 21 and in the z direction towards andaway from it. If the outputs of the individual detectors 23a are summedtogether, this apparatus can operate as described with reference to FIG.1; but the possibility of analysing the information available from theouter fibers 15 individually also enables information to be gatheredrelating to local inclination as well as height of the surface 21.

In another modification within the scope of the invention, a probeaccording to the invention may include a plurality of bundles of fibers,each with its light source, so that parallel sets of measurements may bemade simultaneously of different parts of the surface 21. In yet anothermodification, shown schematically in FIG. 6, the optical fibers 14 and15 are replaced by a solid-state camera detector array 32 having a largenumber of individual detector cells, in rows and columns, which areorganized in groups each having a central cell and a plurality ofsurrounding outer cells. For example, each group may be a 3×3 block ofcells, with one central cell surrounded by eight outer cells. Anillumination array 33, via the beam splitter 18 and lens unit 12,provides on the surface 21 being examined a pattern of illuminated spotswhich, if the surface is positioned such that the spots are sharplyfocussed on it, are in turn sharply imaged only on the central cells,and not on the outer cells, of the groups in the detector array 32. Theoutputs from all the cells of the array 32 are then converted to digitalform using a frame store 34, and transferred to a computer 35 capable ofanalysing the data to produce a contour map or other representation(e.g. a perspective map) of the surface 21.

We claim:
 1. Surface-measuring apparatus comprising a probe and meansfor moving the probe towards and away from a surface under examinationand for monitoring such movement, the probe comprising:a plurality ofclosely spaced light-collecting elements arranged in a light-collectingplane, lens means positioned to produce a sharply focused image of saidlight-collecting elements at an image plane movable relative to saidsurface by movement of the probe, illuminating means so arranged thatthe lens means forms an illuminated spot image of the illuminating meansin the image plane in coincidence with the image in the image plane ofone of the light-collecting elements, means for measuring the incidenceof light which is reflected from a surface under examination on the oneof the light-collecting elements and on surrounding ones of thoseelements, and means for comparing the measured incidence of light onsaid one of the light-collecting elements with the measured incidence oflight on said surrounding ones of said elements.
 2. Surface-measuringapparatus as claimed in claim 1, further comprising a bundle of opticalfibers, each optical fiber having one end exposed at an end plane of thebundle and constituting a respective one of the light-collectingelements, the fibers being connected at their other ends to photodiodesor other photodetector means for measuring the incidence of light on theexposed ends of the fibers.
 3. Surface-measuring apparatus as claimed inclaim 2, wherein the illuminating means comprises a source ofillumination coupled to the other end of the one of the optical fiberswhose said one end constitutes the one of the light-collecting elements.4. Surface-measuring apparatus as claimed in claim 1 or claim 2, whereinthe illuminating means is physically separate from the light-collectingelements and there is interposed between the lens and thelight-collecting elements a beam splitter which is so positionedrelative to the illuminating means that an image of said illuminatingmeans in the beam splitter is superimposed on the one of thelight-collecting elements.
 5. Surface-measuring apparatus as claimed inclaim 1, wherein the light-collecting elements are individual detectorcells forming a detector array of a solid state camera, the detectorcells of the array being organized in groups each having a central celland a plurality of surrounding cells.
 6. Surface-measuring apparatus asclaimed in claim 2, wherein the bundle of optical fibers comprises acentral optical fiber surrounded by six optical fibers spaced at regularintervals around the central optical fibers.
 7. Surface-measuringapparatus as claimed in claim 1, wherein the comparing means includesmeans for producing a difference signal from the measured incidence oflight on said one of the light-collecting elements and the measuredincidence of light on said surrounding ones of said elements, saidmoving means being controlled in accordance with the difference signalto maintain the probe at a substantially constant distance from asurface under examination.
 8. Surface-measuring apparatus as claimed inclaim 7, wherein said distance is such that the image plane is notcoincident with the surface under examination.
 9. A method of measuringthe form of a surface using a probe having lens means and a plurality ofclosely spaced light-collecting elements arranged in a light-collectingplane, the method comprising the steps of:positioning the lens means toproduce a sharply focused image of said light-collecting elements at animage plane movable relative to said surface by movement of the probe,forming with the lens an illuminated spot image in an image plane incoincidence with the image in the image plane of one of thelight-collecting elements, measuring the incidence of light which isreflected from the surface on the one of the light-collecting elementsand on surrounding ones of those elements, and comparing the measuredincidence of light on said one of the light-collecting elements with themeasured incidence of light on said surrounding ones of said elements.10. A method according to claim 9, wherein the light-collecting elementscomprise a bundle of optical fibers.
 11. A method according to claim 10,wherein the spot image is produced by a source of illumination coupledto the other end of the one of the optical fibers whose said one endconstitutes the one of the light-collecting elements.
 12. A methodaccording to claim 9, wherein the spot image is produced by illuminatingmeans which is physically separate from the light-collecting elements,the illuminating means directing light through a beam splitterinterposed between the lens and the light-collecting elements, the beamsplitter being so positioned relative to the illuminating means that animage of said illuminating means in the beam splitter is superimposed onthe one of the light-collecting elements.
 13. A method as claimed inclaim 9, including the step of producing a difference signal from themeasured incidence of light on said one of the light-collecting elementsand the measured incidence of light on said surrounding ones of saidelements, and controlling the movement of the probe in accordance withthe difference signal to maintain the probe at a substantially constantdistance from a surface under examination.
 14. A method according toclaim 13, wherein said distance is such that the image plane is notcoincident with the surface under examination.